Question

During a recent men’s college basketball season, the Villanova Wildcats averaged 22.1 personal fouls per 40 minute game. Assume the time between personal fouls follows an exponential distribution.
a. What is the probability that the next personal foul committed by Villanova will occur within the first minute of a game?
b. What is the probability that the next personal foul committed by Villanova will occur between the first 2 and 4 minutes of a game?
c. What is the probability that the next personal foul committed by Villanova will occur more than 3 minutes after the start of a game?
d. Use Excel to verify the results from parts a and b.
e. What is the standard deviation for this distribution?